Upstairs is a bit more quiet, as someone pointed out. The waiters glide around, making the crepes, pouring wine, etc. Downstairs, I felt a bit mroe bustle, the lights are brighter and it may be a tad louder. Neither really screams out at me, "please take a kid here, for the love of all things Disney!" But I don't see why a child couldn't have a nice sit-down meal with his/her family in either location, as well. If they need constant stimuli to keep them in their seats and mildly behaved, I would venture to guess you wouldn't be considering either option, in the first place.
They are both restaurants, and both lack any entertainment specifically geared towards children- no characters, rides, flashing lights or TV monitors. I believe that in Chefs, people have reported seeing that statue-character from the glass dining room. But upstairs you can get a half-way decent view of Illuminations. One child may be comfortable in both, another may be comfortable in neither. Tell us what things make your children feel "in place" and perhaps we can share with you our own opinions.
Personally, if my children were well behaved, I would gladly take them to as many different restaurants as possible. And in that case, I would opt for Bistro (not because Chefs is bad, but we found Bistro better, IMHO). However, I have no children, so it's not yet an issue.....
Yours is a question with many possible answers.
Andrew